On an equivalence of system-theoretical and categorical concepts

Jiří Adámek; Hartmut Ehrig; Věra Trnková

Kybernetika (1980)

  • Volume: 16, Issue: 5, page (389)-410
  • ISSN: 0023-5954

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Adámek, Jiří, Ehrig, Hartmut, and Trnková, Věra. "On an equivalence of system-theoretical and categorical concepts." Kybernetika 16.5 (1980): (389)-410. <http://eudml.org/doc/28333>.

@article{Adámek1980,
author = {Adámek, Jiří, Ehrig, Hartmut, Trnková, Věra},
journal = {Kybernetika},
keywords = {categorical model of system theory; minimal reduction; minimal realization; Nerode equivalence; systems in a category},
language = {eng},
number = {5},
pages = {(389)-410},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On an equivalence of system-theoretical and categorical concepts},
url = {http://eudml.org/doc/28333},
volume = {16},
year = {1980},
}

TY - JOUR
AU - Adámek, Jiří
AU - Ehrig, Hartmut
AU - Trnková, Věra
TI - On an equivalence of system-theoretical and categorical concepts
JO - Kybernetika
PY - 1980
PB - Institute of Information Theory and Automation AS CR
VL - 16
IS - 5
SP - (389)
EP - 410
LA - eng
KW - categorical model of system theory; minimal reduction; minimal realization; Nerode equivalence; systems in a category
UR - http://eudml.org/doc/28333
ER -

References

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  1. J. Adámek, Realization theory for automata in categories, J. Pure Appl. Algebra 9 (1977), 281-296. (1977) MR0460410
  2. J. Adámek, Categorical realization theory II. Nerode equivalences, In: Algebraische Modele, Kategorien und Gruppoide (H.-J. Hoehnke, ed.). Akademie-Verlag, Berlin 1979, 123- 136. (1979) MR0569581
  3. J. Adámek V. Trnková, Varietors and machines, Technical Rep. 78 - 6, Univ. of Massachusetts, Amherst, 1978 (to appear in Algebra Universalis). (1978) MR0631413
  4. B. D. O. Anderson M. A. Arbib E. G. Manes, Foundations of system theory: finitary and infinitary conditions, Lect. Notes Econ. Math. Syst. 115, Springer-Verlag, Berlin-Heidelberg-New York 1976. (1976) MR0527292
  5. M. A. Arbib E. G. Manes, Fuzzy machines in a category, Bull. Austral. Mathem. Soc. 13 (1975), 169-210. (1975) MR0407106
  6. M. Barr, Right exact functors, J. Pure Appl. Algebra 5 (1974), 1-7. (1974) Zbl0281.18003MR0374239
  7. H. Ehring H.-J. Kreowski, The skeleton of minimal realization, In: Algebraische Modelle, Kategorien und Gruppoide (H.-J. Hoehnke, ed.). Akademie-Verlag, Berlin 1979, 137 - 154. (1979) MR0569582
  8. H. Ehring W. Kühnel, Categorical approach to non-linear constant continuous-time systems, Technical Rep. 76 - 05, University of Berlin (to appear in RAIRO). 
  9. H. Ehring K. D. Kiermeier H.-J. Kreowski W. Kühnel, Universal Theory of Automata, a Categorical Approach, Teubner-Verlag, Stuttgart 1974. (1974) MR0382387
  10. J. A. Goguen, Systems and minimal realization, Proc. 1974 IEEE Conf. Decision Contr., 42-46. (1974) 
  11. H. Herrlich, Factorization of morphisms f : B F A , Math. Z. 114 (1970), 180-186. (1970) 
  12. R. E. Kalman P. L. Falb M. A. Arbib, Topics in Mathematical Systems Theory, McGraw-Hill, New York 1969. (1969) MR0255260
  13. V. Trnková, On minimal realizations of behavior maps in categorical automata theory, Comment. Math. Univ. Carolinae 15 (1974), 555-566. (1974) MR0352205
  14. V. Trnková, Automata and Categories, In: Mathematical Foundations of Comp. Science. (Lect. Notes in Comp. Science 32.) Springer-Verlag, Berlin-Heidelberg-New York 1975, 138-152. (1975) MR0393175
  15. V. Trnková J. Adámek, Realization is not universal, Weiterbildungszentrum für mathematische Kybernetik und Rechentechnik TU Dresden, Heft 21 (1977), 38 - 55. (1977) MR0498783

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